Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s<sup>2</sup> giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Accessing Prior Knowledge

Before the start of the lesson, I cut out the Symmetry Slips so I can provide one set of slips for each pair of students in the class.

Once students are paired up, I hand each pair a set of slips and ask that together they fold each figure at their "lines of symmetry" or "reflecting lines". I inform the learners that figures may have none, one, or more than one reflecting line.

The activity activates some prior knowledge and sets them up for this introductory lesson on quadratics.

Symmetry Slips.docx

New Info

10 minutes

For this lesson I will use this section to introduce vocabulary relevant to the lesson, via a short Vocabulary PowerPoint presentation. I strongly suggest to my students that they not only enter terms in their notebooks, but also add a sketch with features labeled. I include a copy some of the slides of the PowerPoint for printing if desired (seePOWERPOINT PRINTS).

Vocabulary ppt.ppt

POWERPOINT PRINTS.docx

Activity

20 minutes

Student continue to work with the same partners from the APK section. I hand each student an ACTIVITY SHEET. One student will handle graphing calculator, while the other sketches and writes. In Question 4, I tell students to use the CALC function of their calculator to verify their answer. i demonstrate how they can evaluate any of the equations for any value of x, so they must be carefully identify the equation they want to evaluate.

For this investigation, I like to let students go through each question pretty much on their own. I encourage them to speak to another pair of students for help before they come to me. Some students usually need help with setting their calculator Window values, so I ask students to teach their partners and their neighbors how to set up the viewing Window for their graphs.

ACTIVITY SHEET.docx

Generalization

15 minutes

To conclude the lesson I break up the pairs and bring students back to a single group. I proceed to write the equation y = ax2 large on the board. I then call on students to answer questions about the graph of this equation. Here are some possible question prompts:

State the vertex of the graph of a quadratic equation in this form

State its axis of symmetry

If the point (-5, -12) is a point on the graph of an equation in this form, name the coordinates of another point on the same graph.

What roles does "a" play when graphing y = ax2

Does "a" change the shape of the parabola? Explain.

I will choose questions based on my observations of the students' work on the Activity and make adjustments based on the flow of conversation.

Homework

I ask students to complete Homework at home to review today's material and prepare for tomorrow's class.